IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v318y2024i3p966-978.html
   My bibliography  Save this article

The digital economy and advertising diffusion models: Critical mass and the Stalling equilibrium

Author

Listed:
  • Feichtinger, Gustav
  • Grass, Dieter
  • Hartl, Richard F.
  • Kort, Peter M.
  • Seidl, Andrea

Abstract

In the digital economy it is frequently observed that products become more valuable the larger is the number of people that use it. To account for such network effects, we introduce a new diffusion equation in a dynamic model of the firm with the aim to obtain the advertising policy that maximizes firm profits. Also an advertising budget is introduced.

Suggested Citation

  • Feichtinger, Gustav & Grass, Dieter & Hartl, Richard F. & Kort, Peter M. & Seidl, Andrea, 2024. "The digital economy and advertising diffusion models: Critical mass and the Stalling equilibrium," European Journal of Operational Research, Elsevier, vol. 318(3), pages 966-978.
    • Handle: RePEc:eee:ejores:v:318:y:2024:i:3:p:966-978
    DOI: 10.1016/j.ejor.2024.05.043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221724004223
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2024.05.043?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chenavaz, Régis Y. & Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M., 2020. "Modeling the impact of product quality on dynamic pricing and advertising policies," European Journal of Operational Research, Elsevier, vol. 284(3), pages 990-1001.
    2. Suresh P. Sethi, 1973. "Optimal Control of the Vidale-Wolfe Advertising Model," Operations Research, INFORMS, vol. 21(4), pages 998-1013, August.
    3. S. A. Ozga, 1960. "Imperfect Markets Through Lack of Knowledge," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 74(1), pages 29-52.
    4. Feichtinger, Gustav & Grass, Dieter & Kort, Peter M. & Seidl, Andrea, 2021. "On the Matthew effect in research careers," Journal of Economic Dynamics and Control, Elsevier, vol. 123(C).
    5. Chenavaz, Régis Y. & Eynan, Amit, 2021. "Advertising, goodwill, and the Veblen effect," European Journal of Operational Research, Elsevier, vol. 289(2), pages 676-682.
    6. Jeffrey Rohlfs, 1974. "A Theory of Interdependent Demand for a Communications Service," Bell Journal of Economics, The RAND Corporation, vol. 5(1), pages 16-37, Spring.
    7. HALKIN, Hubert, 1974. "Necessary conditions for optimal control problems with infinite horizons," LIDAM Reprints CORE 193, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Gustav Feichtinger & Richard F. Hartl & Suresh P. Sethi, 1994. "Dynamic Optimal Control Models in Advertising: Recent Developments," Management Science, INFORMS, vol. 40(2), pages 195-226, February.
    9. Herbert Dawid & Reinhold Decker & Thomas Hermann & Hermann Jahnke & Wilhelm Klat & Rolf König & Christian Stummer, 2017. "Management science in the era of smart consumer products: challenges and research perspectives," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(1), pages 203-230, March.
    10. Fred M. Feinberg, 2001. "On Continuous-Time Optimal Advertising Under S-Shaped Response," Management Science, INFORMS, vol. 47(11), pages 1476-1487, November.
    11. Yanwu Yang & Baozhu Feng & Joni Salminen & Bernard J. Jansen, 2022. "Optimal advertising for a generalized Vidale–Wolfe response model," Electronic Commerce Research, Springer, vol. 22(4), pages 1275-1305, December.
    12. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    13. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    14. Christophe Van den Bulte & Yogesh V. Joshi, 2007. "New Product Diffusion with Influentials and Imitators," Marketing Science, INFORMS, vol. 26(3), pages 400-421, 05-06.
    15. M. L. Vidale & H. B. Wolfe, 1957. "An Operations-Research Study of Sales Response to Advertising," Operations Research, INFORMS, vol. 5(3), pages 370-381, June.
    16. Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Hartl, Richard F. & Kort, Peter M. & Seidl, Andrea, 2017. "Interaction of pricing, advertising and experience quality: A dynamic analysis," European Journal of Operational Research, Elsevier, vol. 256(3), pages 877-885.
    17. Gila E. Fruchter & Ashutosh Prasad & Christophe Van den Bulte, 2022. "Too Popular, Too Fast: Optimal Advertising and Entry Timing in Markets with Peer Influence," Management Science, INFORMS, vol. 68(6), pages 4725-4741, June.
    18. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-272, March.
    19. Forster, Bruce A., 1975. "Optimal pollution control with a nonconstant exponential rate of decay," Journal of Environmental Economics and Management, Elsevier, vol. 2(1), pages 1-6, September.
    20. Evans David S. & Schmalensee Richard, 2010. "Failure to Launch: Critical Mass in Platform Businesses," Review of Network Economics, De Gruyter, vol. 9(4), pages 1-28, December.
    21. Fruchter, Gila E. & Van den Bulte, Christophe, 2011. "Why the Generalized Bass Model leads to odd optimal advertising policies," International Journal of Research in Marketing, Elsevier, vol. 28(3), pages 218-230.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Schouten, Jop & Cognolato, Davide & Borm, Peter & Cruijssen, Frans, 2024. "Technology Selection with Peer-Based Network Effects," Other publications TiSEM f0f45255-e4f9-44ad-8679-d, Tilburg University, School of Economics and Management.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. El Ouardighi, Fouad & Feichtinger, Gustav & Grass, Dieter & Hartl, Richard & Kort, Peter M., 2016. "Autonomous and advertising-dependent ‘word of mouth’ under costly dynamic pricing," European Journal of Operational Research, Elsevier, vol. 251(3), pages 860-872.
    2. Abedi, Vahideh Sadat, 2019. "Compartmental diffusion modeling: Describing customer heterogeneity & communication network to support decisions for new product introductions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    3. Fred M. Feinberg, 2001. "On Continuous-Time Optimal Advertising Under S-Shaped Response," Management Science, INFORMS, vol. 47(11), pages 1476-1487, November.
    4. Kannan Nilakantan & Subodh Suhas Tagare & Santhi Perumal & Shyam Sreekumaran Nair, 2024. "Is there an optimal market withdrawal decision? A simple mathematical model and analysis," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 51(4), pages 437-468, December.
    5. Vahideh Sadat Abedi & Oded Berman & Dmitry Krass, 2014. "Supporting New Product or Service Introductions: Location, Marketing, and Word of Mouth," Operations Research, INFORMS, vol. 62(5), pages 994-1013, October.
    6. Feichtinger, Gustav & Grass, Dieter & Kort, Peter M. & Seidl, Andrea, 2021. "On the Matthew effect in research careers," Journal of Economic Dynamics and Control, Elsevier, vol. 123(C).
    7. Luzon, Yossi & Pinchover, Rotem & Khmelnitsky, Eugene, 2022. "Dynamic budget allocation for social media advertising campaigns: optimization and learning," European Journal of Operational Research, Elsevier, vol. 299(1), pages 223-234.
    8. Huang, Jian & Leng, Mingming & Liang, Liping, 2012. "Recent developments in dynamic advertising research," European Journal of Operational Research, Elsevier, vol. 220(3), pages 591-609.
    9. Dengpan Liu & Subodha Kumar & Vijay S. Mookerjee, 2012. "Advertising Strategies in Electronic Retailing: A Differential Games Approach," Information Systems Research, INFORMS, vol. 23(3-part-2), pages 903-917, September.
    10. Yegorov, Yury & Wirl, Franz & Grass, Dieter & Eigruber, Markus & Feichtinger, Gustav, 2022. "On the matthew effect on individual investments in skills in arts, sports and science," Journal of Economic Behavior & Organization, Elsevier, vol. 196(C), pages 178-199.
    11. Chaab, Jafar & Salhab, Rabih & Zaccour, Georges, 2022. "Dynamic pricing and advertising in the presence of strategic consumers and social contagion: A mean-field game approach," Omega, Elsevier, vol. 109(C).
    12. Kamihigashi, Takashi, 2005. "Necessity of the transversality condition for stochastic models with bounded or CRRA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 29(8), pages 1313-1329, August.
    13. Antonio Ladrón-de-Guevara & William Putsis, 2015. "Multi-Market, Multi-Product New Product Diffusion: Decomposing Local, Foreign, and Indirect (Cross-Product) Effects," Customer Needs and Solutions, Springer;Institute for Sustainable Innovation and Growth (iSIG), vol. 2(1), pages 57-70, March.
    14. Yan, Yingchen & Zhao, Qiuhong & Qin, Zhongfeng & Sun, Gaoji, 2022. "Integration of development and advertising strategies for multi-attribute products under competition," European Journal of Operational Research, Elsevier, vol. 300(2), pages 490-503.
    15. Weber, Thomas A., 2006. "An infinite-horizon maximum principle with bounds on the adjoint variable," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 229-241, February.
    16. Seidl, Andrea & Caulkins, Jonathan P. & Hartl, Richard F. & Kort, Peter M., 2018. "Serious strategy for the makers of fun: Analyzing the option to switch from pay-to-play to free-to-play in a two-stage optimal control model with quadratic costs," European Journal of Operational Research, Elsevier, vol. 267(2), pages 700-715.
    17. Huini Zhou & Guo Li & Yong Tan & Xu Guan, 2025. "Dynamic investment in online advertising of multi-oligopoly competitive enterprises with spillover effect," Annals of Operations Research, Springer, vol. 344(2), pages 1057-1099, January.
    18. Salhab, Rabih & Le Ny, Jérôme & Malhamé, Roland P. & Zaccour, Georges, 2022. "Dynamic marketing policies with rating-sensitive consumers: A mean-field games approach," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1079-1093.
    19. Temponi, Cecilia & Bryant, Michael D. & Fernandez, Benito, 2009. "Integration of business function models into an aggregate enterprise systems model," European Journal of Operational Research, Elsevier, vol. 199(3), pages 793-800, December.
    20. Du, Rong & Hu, Qiying & Ai, Shizhong, 2007. "Stochastic optimal budget decision for advertising considering uncertain sales responses," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1042-1054, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:318:y:2024:i:3:p:966-978. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.